Second-order discretization schemes of stochastic differential systems for the computation of the invariant law

Abstract

Abstract We Discretize in Time With Step-Size h a Stochastic Differential Equation Whose Solution has a Unique Invariant Probability Measure is the Solution of the Discretized System, we Give an Estimate of in Terms of h for Several Discretization Methods. In Particular, Methods Which are of Second Order for the Approximation of in Finite Time are Shown to be Generically of Second Order for the Ergodic Criterion(1). Keywords: Stochastic differential equationinvariant measurenumerical methodsdiscretization